Missing observations in Youden square designs

The reduction in efficiency in estimating treatment differences in Youden square designs from which individual observations have been lost is considered. A simple generalised inverse of the associated information matrix is used to develop expressions for the variances of the pairwise treatment comparisons. Results on the robustness of Youden squares to the loss of one or two observations are given, and it is shown that for two observations missing there are eight possible cases of resulting design which need to be considered. The frequencies of these cases depend on the form of the initial design, as well as on the design parameters. Examples of similar designs are used to illustrate these different frequencies of resulting designs